If you're constantly moving and switching towers, I believe your IP address can change. It's been awhile since I've did that though, and since I'm overseas right now, I have no way to check it myself.
However, I do know this: If you stay put, and your signal isn't being passed from tower to tower, you will retain the same IP address. For how long, I don't know exactly. But it won't change with every page you load or anything.
To force a new IP, simply put your phone into airplane mode. Wait for the radios to be turned off. As soon as they're off and the airplane mode icon appears, enable the radios again. New IP address.
Although, perhaps "different" is a better word than "new," as, of course, Verizon does have a finite number of IP addresses. However, I tethered my phone to my PC when I needed a bunch of IP addresses for a certain website. I went through 600+ IPs without a single duplicate. They all returned to somewhere in Ohio, so I'm guessing the IP addresses you will be assigned are regional. Would make sense, speed-wise.
